{"id":"https://openalex.org/W4414375123","doi":"https://doi.org/10.1002/qre.70078","title":"MGFM: Modified Gray Genetic Forecast Method for Achieving Sample Expansion and Improving the Weibull Parameter Estimation Performance With Small Samples","display_name":"MGFM: Modified Gray Genetic Forecast Method for Achieving Sample Expansion and Improving the Weibull Parameter Estimation Performance With Small Samples","publication_year":2025,"publication_date":"2025-09-20","ids":{"openalex":"https://openalex.org/W4414375123","doi":"https://doi.org/10.1002/qre.70078"},"language":"en","primary_location":{"id":"doi:10.1002/qre.70078","is_oa":false,"landing_page_url":"https://doi.org/10.1002/qre.70078","pdf_url":null,"source":{"id":"https://openalex.org/S165633816","display_name":"Quality and Reliability Engineering International","issn_l":"0748-8017","issn":["0748-8017","1099-1638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quality and Reliability Engineering International","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101464038","display_name":"Jianyi Gu","orcid":"https://orcid.org/0009-0002-8408-918X"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianyi Gu","raw_affiliation_strings":["School of Mechanical Engineering and Automation Northeastern University  Shenyang China"],"raw_orcid":"https://orcid.org/0009-0002-8408-918X","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation Northeastern University  Shenyang China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xiangwei Kong","orcid":"https://orcid.org/0000-0001-9300-2256"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiangwei Kong","raw_affiliation_strings":["Key Laboratory of Vibration and Control of Aero\u2010Propulsion System Ministry of Education Northeastern University  Shenyang China","Liaoning Province Key Laboratory of Multidisciplinary Design Optimization of Complex Equipment Northeastern University  Shenyang China","School of Mechanical Engineering and Automation Northeastern University  Shenyang China"],"raw_orcid":"https://orcid.org/0000-0001-9300-2256","affiliations":[{"raw_affiliation_string":"Key Laboratory of Vibration and Control of Aero\u2010Propulsion System Ministry of Education Northeastern University  Shenyang China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Liaoning Province Key Laboratory of Multidisciplinary Design Optimization of Complex Equipment Northeastern University  Shenyang China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"School of Mechanical Engineering and Automation Northeastern University  Shenyang China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107049640","display_name":"Jin Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Guo","raw_affiliation_strings":["School of Mechanical Engineering and Automation Northeastern University  Shenyang China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation Northeastern University  Shenyang China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100363325","display_name":"Youguang Guo","orcid":"https://orcid.org/0000-0001-6182-0684"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"You Guo","raw_affiliation_strings":["School of Mechanical Engineering and Automation Northeastern University  Shenyang China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation Northeastern University  Shenyang China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091550885","display_name":"Zinan Wang","orcid":"https://orcid.org/0000-0002-6924-3428"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zinan Wang","raw_affiliation_strings":["School of Mechanical Engineering and Automation Northeastern University  Shenyang China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation Northeastern University  Shenyang China","institution_ids":["https://openalex.org/I9224756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I9224756"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22743475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"1","first_page":"290","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9276000261306763,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9276000261306763,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.927299976348877,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9266999959945679,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.6692000031471252},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.521399974822998},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.48010000586509705},{"id":"https://openalex.org/keywords/shape-parameter","display_name":"Shape parameter","score":0.4643000066280365},{"id":"https://openalex.org/keywords/genetic-algorithm","display_name":"Genetic algorithm","score":0.42419999837875366},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.41519999504089355},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.3472000062465668},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.34380000829696655}],"concepts":[{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.6692000031471252},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4952000081539154},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.48010000586509705},{"id":"https://openalex.org/C199435849","wikidata":"https://www.wikidata.org/wiki/Q3179293","display_name":"Shape parameter","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.42419999837875366},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4203000068664551},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.41519999504089355},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40799999237060547},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3736000061035156},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31790000200271606},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2987000048160553},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27950000762939453},{"id":"https://openalex.org/C137668524","wikidata":"https://www.wikidata.org/wiki/Q189813","display_name":"Censoring (clinical trials)","level":2,"score":0.27469998598098755}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/qre.70078","is_oa":false,"landing_page_url":"https://doi.org/10.1002/qre.70078","pdf_url":null,"source":{"id":"https://openalex.org/S165633816","display_name":"Quality and Reliability Engineering International","issn_l":"0748-8017","issn":["0748-8017","1099-1638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quality and Reliability Engineering International","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4355772197","display_name":null,"funder_award_id":"J2019V00090103","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6508925701","display_name":null,"funder_award_id":"SQ2019YFB 170107","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1966553411","https://openalex.org/W1976004269","https://openalex.org/W1984838906","https://openalex.org/W1991172462","https://openalex.org/W1995263220","https://openalex.org/W1995525894","https://openalex.org/W2001664936","https://openalex.org/W2034758508","https://openalex.org/W2062279503","https://openalex.org/W2063257812","https://openalex.org/W2069837130","https://openalex.org/W2070527826","https://openalex.org/W2074364289","https://openalex.org/W2083663292","https://openalex.org/W2088702111","https://openalex.org/W2113040553","https://openalex.org/W2136917028","https://openalex.org/W2152317228","https://openalex.org/W2154893781","https://openalex.org/W2222914619","https://openalex.org/W2300587709","https://openalex.org/W2432465520","https://openalex.org/W2525826441","https://openalex.org/W2619263008","https://openalex.org/W2727420541","https://openalex.org/W2792548242","https://openalex.org/W2807930787","https://openalex.org/W2883911124","https://openalex.org/W2947861992","https://openalex.org/W3037033368","https://openalex.org/W3103930807","https://openalex.org/W3135262623","https://openalex.org/W3156139896","https://openalex.org/W3170285945","https://openalex.org/W3186037710","https://openalex.org/W3203447806","https://openalex.org/W4206986444","https://openalex.org/W4224240610","https://openalex.org/W4285278718","https://openalex.org/W4292212577","https://openalex.org/W4292830481","https://openalex.org/W4294113398","https://openalex.org/W4294691574","https://openalex.org/W4308151826","https://openalex.org/W4366602292","https://openalex.org/W4367043230","https://openalex.org/W4383337098","https://openalex.org/W4389053130","https://openalex.org/W4389778232","https://openalex.org/W4390064131","https://openalex.org/W4390612801","https://openalex.org/W4391611972","https://openalex.org/W4391737987","https://openalex.org/W4392196631","https://openalex.org/W4403537606"],"related_works":[],"abstract_inverted_index":{"ABSTRACT":[0],"As":[1],"the":[2,8,21,38,51,92,95,97,165,176,186,192,196,200,208,216],"theoretical":[3],"basis":[4],"of":[5,26,42,53,94,185,218],"reliability":[6,25,182],"analysis,":[7],"Weibull":[9,43],"distribution":[10],"is":[11,71,83,100],"widely":[12],"used":[13],"to":[14,20,49,163],"process":[15],"life":[16,31],"data.":[17],"However,":[18],"due":[19],"increasing":[22],"cost":[23],"and":[24,40,154,168,181,211],"mechanical":[27],"products,":[28],"only":[29],"few":[30],"failure":[32],"data":[33],"can":[34,198],"be":[35],"collected,":[36],"while":[37],"accuracy":[39],"stability":[41],"parameter":[44,54,87,169,201],"estimation":[45,55,132,170,202],"become":[46],"inferior.":[47],"Therefore,":[48],"improve":[50,199],"performance":[52,184,203],"with":[56,78,102],"small":[57],"samples,":[58],"a":[59],"new":[60],"sample":[61,105],"expansion":[62,106],"method":[63,69,82],"called":[64],"modified":[65,79],"gray":[66,75],"genetic":[67,76],"forecast":[68],"(MGFM)":[70],"proposed.":[72],"The":[73,172],"hybrid":[74],"algorithm":[77],"maximum":[80],"likelihood":[81],"employed":[84],"for":[85,90],"explicit":[86],"estimation.":[88],"Moreover,":[89],"enhancing":[91],"credibility":[93],"study,":[96],"proposed":[98],"MGFM":[99,190,197,219],"compared":[101],"three":[103,121],"existing":[104],"methods":[107],"(midpoint":[108],"interpolation":[109,113,116],"method,":[110,114],"golden":[111],"section":[112],"mean\u2010variance":[115],"method)":[117],"as":[118,120],"well":[119],"machine":[122],"learning":[123],"algorithms":[124],"(particle":[125],"swarm":[126],"optimization":[127],"(PSO)":[128],"algorithm,":[129,134],"adaptive":[130],"moment":[131],"(ADAM)":[133],"fish":[135],"school":[136],"search":[137],"(FSS)":[138],"algorithm).":[139],"Then,":[140],"seven":[141],"evaluation":[142,183],"parameters":[143],"are":[144,161,191,213,222],"selected,":[145],"including":[146],"mean":[147,150],"absolute":[148],"deviation,":[149],"root":[151],"square":[152],"error,":[153],"so":[155],"on.":[156],"Subsequently,":[157],"Monte\u2010Carlo":[158],"sampling":[159],"simulations":[160],"performed":[162],"obtain":[164],"post\u2010expansion":[166,187],"samples":[167,188],"results.":[171],"results":[173],"show":[174],"that":[175],"accuracy,":[177],"stability,":[178],"fitting":[179],"degree,":[180],"using":[189],"best,":[193],"which":[194],"indicates":[195],"in":[204,220],"simulation":[205],"experiments.":[206],"Then":[207],"extended":[209],"applications":[210],"challenges":[212],"discussed.":[214],"Finally,":[215],"advantages":[217],"engineering":[221],"illustrated":[223],"by":[224],"two":[225],"examples.":[226]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}